Definition
Local-nonsatiation
MWG- Definition 3.B.3
The preference relation 
on X is locally nonsatiated if for any x 
X and every 
> 0, there is y 
X such that || y - x || 
and y 
x.
It is a weaker desirability assumption than monotonicity.
Interpretation
For any consumption bundle 
, within any small distance away from x, there is another bundle 
that is preferred to x.
Proposition
The local nonsatiation and monotonicity rules out (exclude) "Thick" indifferent set.
Or that there is not a distance a that exists || y - x || 
a and y 
x.
Note
- || y - x || is the Euclidean distance between points x and y.